5 pencils and 7 pens together cost ₹50, whereas 7 pencils and 5 pens together cost ₹46. Find the cost of each pencil and pen.
Answer: Pencil ₹3, pen ₹5.
Step-by-step solution
Idea: Again the coefficients are swapped, so add and subtract the equations.
- Pencil ₹x, pen ₹y: 5x + 7y = 50 … (1), 7x + 5y = 46 … (2).1 mark
- Add: 12x + 12y = 96 ⇒ x + y = 8 … (3). Subtract (1) from (2): 2x − 2y = −4 ⇒ x − y = −2 … (4).1 mark
- (3) + (4): 2x = 6 ⇒ x = 3; y = 5. Pencil ₹3, pen ₹5.1 mark
A pencil costs ₹3 and a pen costs ₹5.
Check: 5(3) + 7(5) = 15 + 35 = 50 ✓; 7(3) + 5(5) = 21 + 25 = 46 ✓.
Answer to write in the exam
5x + 7y = 50 … (1); 7x + 5y = 46 … (2)
(1) + (2): 12x + 12y = 96 ⇒ x + y = 8 … (3)
(2) − (1): 2x − 2y = −4 ⇒ x − y = −2 … (4)
(3) + (4): 2x = 6 ⇒ x = 3; y = 5
∴ Pencil = ₹3, pen = ₹5
Common mistakes that cost marks
- Subtracting (2) − (1) and writing 2x − 2y = 4: the right side is 46 − 50 = −4.
- Swapping the final prices.
How this can come in the exam
MCQ (1 mark)
3 apples and 4 oranges cost ₹60; 4 apples and 3 oranges cost ₹66. One apple costs
- ₹6
- ₹12
- ₹9
- ₹8
Show answer
(B) ₹12
Add: x + y = 18; subtract: x − y = 6 ⇒ x = 12.
Try one yourself
4 erasers and 3 sharpeners cost ₹31; 3 erasers and 4 sharpeners cost ₹32. Find each price.
Show answer
x + y = 9, x − y = −1 ⇒ eraser ₹4, sharpener ₹5.
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